Approximating common fixed points of finite family of asymptotically nonexpansive non-self mappings

Approximating Common Fixed Points of Finite Family of Asymptotically Nonexpansive Non-self Mappings

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, . . . , TN : K −→ E be N asymptotically nonexpansive nonself mappings with sequences {r n} such that ∑∞ n=1 r n < ∞, for all 1 ≤ i ≤ N and F = ∩i=1F (Ti) 6= φ. Let {α n}, {β n} and {γ n} are sequences in [0, 1] with α n + β i n + γ i n = 1 for all i =...

A new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces

In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.

Approximating fixed points of generalized nonexpansive mappings

Approximating Fixed Points of Total Asymptotically Nonexpansive Mappings

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E , which is also a nonexpansive retract of E with nonexpansive retraction P . Let {Ti : i ∈ I } be N nonself asymptotically nonexpansive mappings from K to E such that F = {x ∈ K : Ti x = x, i ∈ I } 6= φ, where I = {1, 2, . . . , N }. From arbitrary x0 ∈ K , {xn} is defined by xn = P((1− αn)xn−1 + αnTn(PT...